Numerical Study of Film Cooling in Oxygen/Methane Thrust Chambers

4 TH EUROPEAN CONFERENCE FOR AEROSPACE SCIENCES Numerical Study of Film Cooling in Oxygen/Methane Thrust Chambers B. Betti, E. Martelli, F. Nasuti and M. Onofri Università di Roma La Sapienza Dipartimento di Ingegneria Meccanica e Aerospaziale, via Eudossiana 18, Roma 00184, Italy Seconda Università di Napoli Dipartimento di Ingegneria Aerospaziale e Meccanica, Via Roma 29, Aversa 81131, Italy Abstract Oxygen/methane propellant combination has recently gained interest for space propulsion as proved by the inclusion of its study in the European Community 7 th Framework Program (FP7) project In-Space Propulsion 1 (ISP-1). In the rocket engine design phase, the different available options for thrust chamber cooling have to be studied. In this framework, the thermo-fluid dynamic analysis of film-cooled thrust chambers is one of the necessary steps for the reliable development of liquid rocket engines. In the present study, thrust chamber film cooling efficiency is analyzed by means of a multi-component Reynolds-Averaged Navier-Stokes (RANS) equations solver. After validation of the simplified approach against available data for oxygen/hydrogen thrust chambers, a preliminary numerical study of the oxygen/methane film-cooled thrust chamber which will be tested in the ISP-1 project is carried out. 1. Introduction The In-Space Propulsion 1 (ISP-1) project founded by the European Community 7 th Framework Program (FP7) has the objective of improving the knowledge of future space mission cryogenic propulsion [1]. One of the goals of this project is to acquire a basic knowledge of low thrust cryogenic oxygen/methane propulsion. Methane as a fuel can provide a higher specific impulse, together with better cooling abilities and less soot deposition than kerosene. Differently than oxygen/hydrogen propellant combination, oxygen/methane can be considered as space storable and is favored by higher density [2], although it gives lower specific impulse. The adequate understanding and accurate prediction of heat transfer characteristics and wall temperature distribution in presence of film cooling are considered key features for the development of reliable oxygen/methane engines. Film cooling in the hot-gas side of thrust chambers is an important technique which can relieve the regenerative cooling system requirements. Film cooling is obtained by injecting a cold gas or liquid tangentially to the wall to protect it from the hot combustion products in the core of the chamber and to keep it under the safe operative temperature. Film injection is provided by a single circumferential slot (curtain cooling) or through a number of finite width slots (slot film cooling). This active cooling technique has been widely adopted for high performance thrust chamber such as Space Shuttle main engine (SSME) and Vulcain 2 for the European launcher Ariane 5. For these engines thermal and structural loads are reduced by the combined use of film and regenerative cooling. The influence of main governing parameters on film cooling efficiency has been included in several analytical models [3, 4, 5, 6]. Air-air and foreign gas-air film cooling have been widely investigated by experimental studies [3], [7] and numerical simulations [8, 9, 10]. Recently, film cooling in oxygen/hydrogen thrust chambers has been investigated by experimental studies [11, 12, 13, 14] and numerical simulations [15, 16, 17, 18]. Film cooling efficiency has been also experimentally investigated for oxygen/kerosene [19] and oxygen/methane [20] propellant combinations. The aim of the present study is to assess the capability of a simplified approach to capture peculiar features of film-cooled thrust chambers in terms of wall heat flux and film cooling efficiency. The simplified approach consists of considering only the main geometrical aspects of the injection plate without introducing any modeling of atomization, vaporization, mixing and combustion. Before analyzing film cooling test cases, a benchmark experimental test case of a nozzle operated with hot air is reproduced to validate the imposed wall temperature boundary condition implemented Copyright 2011 by B. Betti, E. Martelli, F. Nasuti and M. Onofri. Published by the EUCASS association with permission.

PP LIQUID PROPULSION ISP 1 in a in-house CFD numerical code. Then, a detailed film cooling experimental test case is reproduced to assess the capability of the simplified approach to evaluate wall heat flux in a liquid oxygen/gaseous hydrogen subscale combustion chamber with and without film cooling. Finally, methane film cooling capability is analyzed reproducing an experimental test case which will be carried out in the frame of the ISP-1 project [1]. 2. Numerical approach The present approach relies on an in-house 3D multi-block finite volume Reynolds-Averaged Navier-Stokes (RANS) equations solver [21], modified to simulate multi-component mixtures of thermally perfect gases. Multi-component diffusion has been validated [22] reproducing two experimental test cases retrieved in open literature. Turbulence is described by means of the Spalart-Allmaras one equation model [23]. A constant turbulent Schmidt number is adopted to model turbulent diffusivity. 3. Validation test cases 3.1 Hot-gas side heat transfer Hot-gas side boundary condition has been validated by reproducing the benchmark experimental test case No. 313 of [24] where wall temperature and wall heat flux measurements are collected. The test case is characterized by a supersonic nozzle where compressed and heated air flows with a stagnation pressure of 11.91 bar and a stagnation temperature of 842.78 K. Wall temperature and wall heat flux measurement uncertainties are ±1% and ±8%, respectively. The numerical reproduction of the experimental test case has been carried out by axis-symmetric computations with grid and boundary conditions shown in Fig. 1. Three grid levels were employed to ensure grid convergence, with the Figure 1: Convergent-divergent nozzle [24]: grid (medium grid level) and boundary conditions enforced. fine grid having 200x180 cells in the axial and radial directions, respectively. The medium grid is obtained by removing one node out of two, in each coordinate direction, from the fine grid. In the same way the coarse grid is obtained from the medium grid. Axial velocity profile in section x = 0.0823 mm and wall heat flux along the nozzle obtained with coarse, medium and fine grids are shown in Fig. 2(a) and Fig. 2(b), respectively. Asymptotic grid convergence is reached and Richardson extrapolated numerical solution [25] is evaluated and plotted. To evaluate the grid independence of the numerical solution, percentage errors of each grid level solution referred to the Richardson extrapolated solution are plotted. Axial velocity profiles show errors lower than 0.5% even with the coarse grid, whereas wall heat flux profiles show errors up to 5% with the coarse grid in the region near the inlet section where boundary layer develops. Comparison 2

B. Betti, E. Martelli, F. Nasuti and M. Onofri - NUMERICAL STUDY OF FILM COOLING IN OXYGEN/METHANE THRUST CHAMBERS (a) Axial velocity profile in section x = 0.0823 mm. (b) Wall heat flux along the chamber Figure 2: Convergent-divergent nozzle [24]: grid verification. Figure 3: Convergent-divergent nozzle [24]: comparison between experimental data and numerical solution. Interpolated wall temperature profile is enforced as a boundary condition. with experimental data [24] is shown in Fig. 3. Note that the wall temperature enforced has been interpolated with a polynomial function in order to have a smooth temperature profile at the wall. The corresponding numerical evaluation of wall heat flux follows the experimental data within the maximum total error (±8%) estimated in the reference work. The comparison shows the capability of the solver to reproduce properly thermal boundary layers near the wall and thus to be employed in the following to evaluate wall heat flux from the hot gases in a combustion chamber to the wall with and without film cooling. 3

PP LIQUID PROPULSION ISP 1 3.2 Wall heat flux in subscale combustion chambers with film cooling The simplified approach to study film cooled thrust chamber is first assessed by reproducing a well documented experimental test case [18, 26, 14]. This test case consists in a water-cooled high pressure subscale combustion chamber operated with liquid oxygen (LOX) and gaseous hydrogen (H 2 ). The combustion chamber features are summarized in Tab. 1. Hydrogen film is injected tangentially to the chamber wall through slots which are arranged in the same azimuthal position of the outer ring injectors. Main parameters of the chosen load point are summarized in Tab. 2. In order to have a reference solution with the same chamber pressure and hot-gas mixture ratio, the same load point is investigated with and without film cooling. Due to the small amount of film injected in the chamber compared to the overall mass flow rate, the difference between the chamber pressure in the case with and without the film is negligible. In the numerical simulations, the three dimensional configuration of Chamber Film Length, L (mm) 200 Inner radius, r c (mm) 25 Throat radius, r th (mm) 16.5 Slot number, N slot 10 Slot height, s (mm) 0.40 Slot width, b (mm) 3.50 With Film Cooling Without Film Cooling p c (MPa) 11.94 11.62 ṁ LOX (kg/s) 3.62 3.61 ṁ H2 (kg/s) 0.60 0.60 ṁ f ilm /(ṁ LOX + ṁ H2 ) (%) 1.83 0.0 T f ilm (K) 287.5 - Table 1: Subscale combustion chamber and film cooling geometrical features [14] Table 2: Film cooling experimental load point [14] with and without film cooling the chamber has been reduced to a two dimensional axis-symmetric configuration as shown in Fig. 4. The simplified approach adopted for the numerical simulations is described in the following. The injector plate near field is not resolved in details and atomization, vaporization, mixing and combustion phenomena are not modeled assuming they are confined near the injector plate. A mixture of equilibrium combustion products is injected in the chamber through the inlet section which is evaluated as the section with the maximum radius covered by the injectors on the injector plate design (hot gas injection section is highlighted in red in Fig. 4). Hydrogen film is injected through the blue section of Fig. 4, which is obtained matching the experimental film cooling slot height and imposing 2D axis-symmetry. With this assumption, experimental film inlet velocity and inlet temperature are matched, whereas experimental film mass flow rate is not reproduced. Goal of the simplified approach is to preserve the main geometrical features of the injector plate such as the distance between outer injector ring and film slot and the film slot height. Figure 4: LOX/H 2 film cooling experimental test bench: from the 3D configuration (experimental setup) to the 2D axis-symmetric configuration (numerical simulation). Hot gas injection : red section; film cooling injection: blue section. (Adapted from [14]). The numerical simulation is carried out on a grid divided into three blocks with different features (Fig. 5). In the first block, cells are clustered radially near the chamber wall and axially near the plate between the hot gas injection and the film injection to resolve boundary layers, cells are also clustered inside the flowfield in the radial direction to resolve 4

B. Betti, E. Martelli, F. Nasuti and M. Onofri - NUMERICAL STUDY OF FILM COOLING IN OXYGEN/METHANE THRUST CHAMBERS Figure 5: LOX/H 2 film cooling experimental test bench [14]: multi-block numerical grid and boundary conditions enforced. Enlargement of the injection block with enforced boundary conditions in the case with and without film cooling. Grid Levels No. of Volumes Block 1 Block 2 Block 3 y min Coarse grid 25x45 15x30 20x20 0.8 µm Medium grid 50x90 30x60 40x40 0.4 µm Fine grid 100x180 60x120 80x80 0.2 µm Table 3: LOX/H 2 film cooling test case [14]: multi-block grid verification. the mixing layer between the film injection and the hot gas injection. In the second and third blocks, cells are clustered radially near the wall to resolve the boundary layer. A similar grid has been employed for the case without film cooling in which the first block has been modified to take into account only for the hot gas injection, whereas blocks 2 and 3 have been left unchanged. Injection block boundary conditions in the case with and without film cooling are shown in Fig. 5. In the subsonic inflow, mass flow rate per unit area, stagnation temperature, velocity direction and mixture composition are imposed for hot gas and film. Hot gas mass flow rate is the sum of oxidizer and fuel mass flow rate from the injectors. The mixture composition and the stagnation temperature at the hot-gas inlet are calculated by the NASA Chemical Equilibrium and Applications (CEA) code, which is a one-dimensional chemical equilibrium calculation program [27], imposing the overall mixture ratio and the chamber pressure and assuming the stagnation temperature equal to the adiabatic flame temperature. Hydrogen film mass flow rate is evaluated by preserving the experimental inlet temperature and velocity considering a 2D axis-symmetric injection. Stagnation temperature is evaluated with an isentropic assumption from film inlet temperature and inlet Mach number. Experimental surface temperatures interpolated along the chamber are enforced at no-slip walls boundaries. In the nozzle, the isothermal wall temperature of 700 K is assigned due to the lack of experimental measurements in this region. Grid asymptotic convergence has been verified with three grid levels whose volumes are summarized per block in Tab. 3. Medium grid size numerical solution differs from Richardson extrapolated solution by an error lower than 1%. The computed temperature field is shown in Fig. 6 for both cases with (top) and without (bottom) film cooling. Enlargements of the inlet section highlight the flowfield structure near the injection region. Large recirculation occurs near the wall in the case without film cooling, whereas a pair of counter rotating vortices takes place between hot gas 5

PP LIQUID PROPULSION ISP 1 Figure 6: LOX/H 2 film cooling test case [14]: temperature field in the case with (top) and without (bottom) film cooling. Enlargements of the inlet region with streamlines. and film injection in the case with film cooling as shown by the superimposed streamlines. Wall heat flux along the chamber with and without film cooling is shown in Fig. 7(a). Filled and empty dots represent wall heat flux experimental measurements by gradient method with and without film cooling, respectively. Error bars (±8%) are included with the estimated error evaluated in [18]. Numerical evaluation for wall heat flux are plotted in solid red and black lines for the case with and without film cooling, respectively. Numerical wall heat flux without film cooling over-predicts experimental measurements near the injector plate (first two measurement points) whereas downstream follows experimental values within experimental errors. On the contrary, wall heat flux with film cooling is largely underestimated due to the larger amount of film injected in the numerical simulation with respect to the experimental value. Nevertheless, numerical solution reproduces the experimental trend as can be seen comparing the red dashed line which represents the experimental trend of the last four measurement points and the red dot-dashed line which represent the numerical trend in the same spatial region. To take into account the three dimensional configuration of the film slots, wall heat flux along the chamber with film cooling has been evaluated by a weighted average ( q w,av ) (blue solid line) between the numerical results obtained in the 2D axis-symmetric configuration with film ( q w,w f ilm ) (red solid line) and without film ( qw,wo f ilm ) (black solid line). Weights are ɛ and (1 ɛ) where ɛ is the surface ratio between total slot width and the overall chamber perimeter per unit length as shown in Eq. 1. Weights adopted in Eq. 1 neglect spanwise diffusion and give an estimation of the maximum wall heat flux achievable with a three dimensional configuration. q w,av = ɛ q w,w f ilm + (1 ɛ) q w,wo f ilm with: ɛ = N slotb 2πr c (1) In both cases (black and blue line), up to the second measurement point numerical solutions largely over-predict experimental data because injector plate near field phenomena are not modeled. In the numerical solution without the film cooling, wall heat flux reflects a backward facing step configuration with two peaks linked to the hot gas recirculation region shown in Fig. 6. In the experimental test, the recirculation region near the injector plate encompasses cold gases and thus wall heat flux smoothly grows along the chamber without peaks. Previous analysis of this simplified approach [22] underlined that after the flow reattachment point, wall heat flux along the chamber follows experimental trend in a similar way. For this reason, the present analysis is focused on the numerical wall heat flux after the flow reattachment point on the wall (located after the second wall heat flux peak). After this point, in both cases numerical 6

B. Betti, E. Martelli, F. Nasuti and M. Onofri - NUMERICAL STUDY OF FILM COOLING IN OXYGEN/METHANE THRUST CHAMBERS (a) Experimental measurements [18] (filled dots with film cooling, empty dots without film cooling) vs numerical solution with (red solid line) and without (black solid line) film cooling. Experimental trend (dashed red line) is evaluated with the last four measurement points. (b) Experimental measurements [18] (filled dots with film cooling; empty dots without film cooling) vs numerical solution with (red) and without (black) film cooling, and weighted averaged numerical solution with film cooling (blue). Error bars in numerical solutions quantify the maximum radiative heat flux. Figure 7: LOX/H 2 film cooling wall heat flux [14] wall heat flux follows experimental data within the experimental error along the chamber. Moreover, a rough estimation of the radiative heat flux coming from the flame has been added to the convective wall heat flux and is shown in Fig. 7(b) as error bars over the solid lines. The maximum radiative heat flux from the hot gas to the wall has been evaluated with Eq. 2 valid for transparent gas and non-emitting walls: q wall, rad = ε g σt 4 Hot Gas (2) where ε g is the effective emissivity of hot gas, σ is the Stefan-Boltzmann constant and T Hot Gas is the maximum temperature in each section. Hot gas is supposed to be transparent in order to evaluate the maximum radiative heat flux coming to the wall from hot gas assuming for each section the maximum gas temperature. Walls are supposed to be non-emitting because in thrust chambers wall temperature is always much lower than hot gas temperature. In high pressure oxygen/hydrogen rocket thrust chambers, combustion products mixture is mainly composed by water vapor and the effective emissivity of this mixture has been evaluated in [28] and is assumed here to be equal to 0.45. With this test case, the capability of the adopted simplified approach to capture peculiar features of film cooled thrust chambers in terms of heat flux has been assessed. This simplified approach is employed in the following section to analyze film cooling efficiency of an oxygen/methane subscale thrust chamber. 4. Film cooling in oxygen/methane thrust chambers In the frame of the 7 th Framework Program within the In-Space Propulsion 1 project, film cooling in oxygen/methane thrust chamber will be studied in terms of experiments and numerical simulations. In particular, the experimental test case [1] consists in a low pressure calorimetric subscale combustion chamber where gaseous oxygen (O 2 ) and gaseous methane (CH 4 ) at ambient temperature are injected. Film cooling is realized with gaseous methane injected through a 2D axis-symmetric circular slot (Tab. 4). In the experimental test campaign, different chamber pressure, mixture ratio and film slot height will be investigated providing axial distribution of heat pick-up based on detailed water mass flow rate and surface temperatures. A preliminary numerical analysis of the wall heat flux and the film cooling efficiency is conducted in the present work of ISP-1 project as a support to the experimental test. In particular, the simplified approach described and verified in Sec. 3.2 is employed to evaluate the film cooling efficiency in the subscale combustion chamber whose test campaign is foreseen to end by the end of the year. One experimental load 7

PP LIQUID PROPULSION ISP 1 Chamber Lenght, L (mm) 200 Inner radius, r c (mm) 25 Throat radius, r th (mm) 14 Chamber Injectors p c 10 bar O/F 3.4 ṁ O2 ṁ CH4 0.26100 kg/s 0.07676 kg/s Film Slot height, s (mm) 0.46 Film ṁ f ilm /ṁ O2 +CH 4 20% Table 4: O 2 /CH 4 subscale chamber and film cooling geometrical features Table 5: O 2 /CH 4 Film Cooling: experimental load point point whose main parameters are summarized in Tab. 5 has been selected within the design test matrix as a reference test case to evaluate film cooling efficiency. Film cooling capabilities of keeping the thrust chamber wall in a safe operative mode are quantified by film cooling efficiency which can be defined [3] as: η = T aw T cc T 2 T cc (3) where T aw is the adiabatic wall temperature, T cc and T 2 are the hot gas and the film cooling temperature, respectively. As can be seen in Fig. 8, numerical grid and boundary conditions are similar to those employed in Sec. 3.2 and described in Fig. 5. The only difference is in the wall boundary condition where for the validation test case in Sec. 3.2 wall temperature was prescribed as an interpolation of experimental surface temperature measurements, whereas in this analysis no-slip walls are treated as adiabatic walls to evaluate film cooling efficiency. The multi-block numerical grid Figure 8: O 2 /CH 4 film cooling experimental test bench: multi-block numerical grid and boundary conditions enforced. Enlargement of the injection block with enforced boundary conditions in the case with and without film cooling. is composed by three blocks with the same features described in Sec. 3.2 for the injection region, the middle region and the nozzle with 70x80, 30x60 and 50x40 volumes, respectively. Temperature field with and without film cooling is described in Fig. 9, with an enlargement of the inlet section whose peculiar flows features are highlighted by superimposed streamlines. In Fig. 10, wall adiabatic temperature has been evaluated with (solid red line) and without (solid green line) film cooling. Film cooling efficiency (solid blue line) is evaluated with Eq. 3. 8

B. Betti, E. Martelli, F. Nasuti and M. Onofri - NUMERICAL STUDY OF FILM COOLING IN OXYGEN/METHANE THRUST CHAMBERS The initial plateau of efficiency near the film injection where wall temperature equals film temperature is so little that cannot be seen in Fig. 10. Then efficiency begins to decrease up to the nozzle. As can be seen adiabatic wall temperatures even with film cooling exceeds by far material allowable temperatures. For this reason, in these experimental configurations convective cooling represents the only way to cool the chamber enough to keep it under safe conditions for the overall test campaign. Figure 9: O 2 /CH 4 film cooling: temperature field with (top) and without (bottom) film cooling. Figure 10: O 2 /CH 4 film cooling: adiabatic wall temperature with (red line) and without (green line) film cooling and film cooling efficiency η f ilm (blue line). 9

PP LIQUID PROPULSION ISP 1 5. Conclusions In this work, the ability of a simplified approach to evaluate numerically wall heat flux in film-cooled rocket thrust chamber is assessed. After validation of the wall boundary condition by reproducing a benchmark test case, the simplified approach is applied to a film cooled LOX/H 2 subscale combustion chamber to evaluate wall heat flux with and without film cooling. In reproducing this test case, a mixture of equilibrium combustion products is injected in the chamber surrounded by a 2D axis-symmetric film cooling. Experimental film injection velocity and temperature, and slot height are reproduced whereas film mass flow rate is higher than the experimental value. Experimental data and numerical solutions for wall heat flux with and without film cooling are in good agreement within the experimental error. Due to the three dimensional configuration of the film injection, numerical wall heat flux has been obtained by a weighted average of 2D axis-symmetric wall heat fluxes with and without film cooling. In addition, the maximum radiative heat transfer from the hot gases has been roughly estimated. Comparison with experimental data gives confidence in the present simplified approach as a tool for a first evaluation of thermal environment of film cooled thrust chambers. Finally, film cooling efficiency in oxygen/methane thrust chambers has been analyzed reproducing a test case designed in the frame of the ISP-1 project. 6. Acknowledgments The present study is being performed within the In-Space Propulsion 1 project coordinated by SNECMA and supported by the European Community 7 th Framework Program for Research and Technology, Grant agreement No. 218849. Part of the numerical simulations presented were done at the CASPUR High Performance Computing (HPC) facilities within the Standard HPC grant of 2011. References [1] Ordonneau, G., Haidn, O., Soller, S., and Onofri, M., Oxygen-methane Combustion Studies in In Space Propulsion Programme, 4th European Conference for Aerospace Sciences, EUCASS, Saint Petersburg, Russia, 3-7 July, 2011. [2] Preuss, A., Preclik, D., Mading, C., Gorgen, J., Soller, S., Haidn, O., Oschwald, M., Clauss, W., Arnold, R., and Sender, J., LOX/Methane Technology Efforts for Future Liquid Rocket Engines, 5th International Spacecraft Propulsion Conference and 2nd International Symposium on Propulsion for Space Transportation, 2008. [3] Goldstein, R. J., Film Cooling, Advances in Heat Transfer, Vol. 7, pp. 321-379, 1971. [4] Simon, F. F., Jet Model for Slot Film Cooling with Effect of Free-stream and Coolant Turbulence, NASA-TP- 2655, 1986. [5] Dellimore, K. H., Cruz, C., Marshall, A. W., and Cadou, C. P., Influence of a Streamwise Pressure Gradient on Film-Cooling Effectiveness, Journal of Thermophysics and Heat Transfer, Vol.23, No.1, Jan-Mar 2009. [6] Dellimore, K. H., Marshall, A. W., and Cadou, C. P., Influence of Compressibility on Film-Cooling Effectiveness, Journal of Thermophysics and Heat Transfer, Vol.24, No.3, Jul-Sep 2010. [7] Cruz, C. A. and Marshall, A. W., Surface and Gas Measurements Along a Film-Cooled Wall, Journal of Thermophysics and Heat Transfer, Vol. 21, No. 1, Jan-Mar 2007. [8] Dellimore, K. H., Marshall, A. W., Trouvé, A., and Cadou, C. P., Numerical Simulation of Subsonic Slot-Jet Film Cooling of an Adiabatic Wall, 47th AIAA Aerospace Science Meeting Including The New Horizons Forum and Aerospace Exposition, 5-8 Jan 2009, Orlando, Florida. AIAA-2009-1577. [9] Dellimore, K. H., Modeling and Simulation of Mixing Layer Flows For Rocket Engine Film Cooling, Ph.D. Dissertation, University of Maryland, 2010. 10

B. Betti, E. Martelli, F. Nasuti and M. Onofri - NUMERICAL STUDY OF FILM COOLING IN OXYGEN/METHANE THRUST CHAMBERS [10] Voegele, A. P., Trouvé, A., Cadou, C., and Marshall, A., RANS Modeling of 2D Adiabatic Slot Film Cooling, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 25-28 July 2010, Nashville, TN - AIAA 2010-6735. [11] Kim, J. G., Lee, K. J., Seo, S., Han, Y. M., Kim, H. J., and Choi, H. S., Film Cooling Effects on Wall Heat Flux of a Liquid Propellant Combustion Chamber, 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 9-12 July 2006, Sacramento, CA. AIAA-2006-5196. [12] Arnold, R., Suslov, D., Haidn, O. J., and Weigand, B., Circumferential Behavior of Tangential Film Cooling and Injector Wall Compatibility in a High Pressure LOX/GH 2 Subscale Combustion Chamber, 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 21-23 July 2008, Hartford, CT, AIAA 2008-5242. [13] Arnold, R., Suslov, D., and Haidn, O. J., Film Cooling of Accelerated Flow in a Subscale Combustion Chamber, Journal of Propulsion and Power Vol.25, No. 2, Mar-Apr 2009. [14] Arnold, R., Suslov, D., and Haidn, O. J., Film Cooling in a High-Pressure Subscale Combustion Chamber, Journal of Propulsion and Power, Vol.26, No. 3, May-Jun 2010. [15] Han, P. G., Namkoung, H. J., Kim, K. H., and Yoon, Y. B., A Study on the Cooling Mechanism in Liquid Rocket Engines, 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 11-14 July 2004, Fort Laudardale, FL. AIAA-2004-3672. [16] Zhang, H. W., Tao, W. Q., He, Y. L., and Zhang, W., Numerical Study of Liquid Film Cooling in a Rocket Combustion Chamber, International Journal of Heat and Mass Transfer, Vol. 49, pp 349-358, 2006. [17] Zhang, H. W., He, Y. L., and Tao, W. Q., Numerical Study of Film and Regenerative Cooling in a Thrust Chamber at High Pressure, Numerical Heat Transfer, Part A, Vol.52, pp 991-1007, 2007. [18] Arnold, R., Suslov, D., Oschwald, M., Haidn, O. J., Aichner, T., Ivancic, B., and Frey, M., Experimentally and Numerically Investigated Film Cooling in a Subscale Rocket Combustion Chamber, 3rd European Conference for Aerospace Sciences (EUCASS), July 2009. [19] Kirchberger, C., Schlieben, G., Hupfer, A., Kau, H., Martin, P., and Soller, S., Investigation on Film Cooling in a Kerosene/GOX Combustion Chamber, 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2-5 August 2009, Denver, CO. AIAA 2009-5406. [20] Arnold, R., Suslov, S., and Haidn, O. J., Experimental Investigation of Film Cooling with Tangential Slot Injection in a LOX/CH4 Subscale Rocket Combustion Chamber, 26th International Symposium on Space Technology and Science (ISTS), 2008. [21] Pizzarelli, M., Nasuti, F., Paciorri, R., and Onofri, M., Numerical Analysis of Three-Dimensional Flow of Supercritical Fluid in Cooling Channels, AIAA Journal, Vol. 47, No. 11 (2534-2543), 2009. [22] Betti, B., Martelli, E., and Nasuti, F., Heat Flux Evaluation in Oxygen/Methane Thrust Chambers by RANS Approach, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 25-28 July 2010, Nashville, TN - AIAA-2010-6721. [23] Spalart, P. and Allmaras, S., A One-equation Turbulence Model for Aerodynamic Flows, La Recherche Aerospatiale 1, 5-23, 1994. [24] Back, L. H., Massier, P. F., and Gier, H. L., Convective Heat Transfer in a Convergent-Divergent Nozzle, NASA Technical Report No. 32-415, 1965. [25] Roy, C. J., McWherter-Payne, M. A., and Oberkampf, W. L., Verification and Validation for Laminar Hypersonic Flowfields, Part 1: Verification, AIAA Journal, Vol. 41, No. 10, October, 2003. [26] Suslov, D. I., Arnold, R., and Haidn, O. J., Investigation of Two Dimensional Thermal Loads in the Region near the Injector Head of a High Pressure Subscale Combustion Chamber, 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum And Aerospace Exposition 5-8 January 2009, Orlando, FL. AIAA-2009-450. 11

PP LIQUID PROPULSION ISP 1 [27] McBride, B. J. and Gordon, S., Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, NASA Reference Publication 1311, 1994. [28] Wang, Q., Wu, F., Zeng, M., Luo, L., and Sun, J., Numerical Simulation and Optimization on Heat Transfer and Fluid Flow in Cooling Channel of Liquid Rocket Engine Thrust Chamber, Engineering Computations: International Journal for Computed-Aided Engineering and Software. Vol. 23 No. 8, pp.907-921, 2006. 12